%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET505-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:17:15 PM UTC 2026
% Result : Unsatisfiable 0.20s 5.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 43 ( 11 unt; 11 nHn; 28 RR)
% Number of literals : 85 ( 26 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(unordered_pair_member,axiom,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(regularity2,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(cartesian_product1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
cnf(unordered_pair3,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(prove_corollary_2_to_universal_class_not_set_1,negated_conjecture,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_universal_class_not_set_1) ).
cnf(c_0_11,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_12,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_13,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_14,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_11 ).
cnf(c_0_15,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_16,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_12 ).
cnf(c_0_17,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_18,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_13 ).
cnf(c_0_19,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_24,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_25,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
regularity2 ).
cnf(c_0_26,plain,
( singleton(X1) = null_class
| regular(singleton(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_27,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_24 ).
cnf(c_0_29,plain,
( singleton(X1) = null_class
| intersection(singleton(X1),X1) = null_class ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_27]),c_0_20]) ).
cnf(c_0_31,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[cartesian_product1]) ).
cnf(c_0_32,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(fof_simplification,[status(thm)],[unordered_pair3]) ).
cnf(c_0_33,plain,
( ~ member(X2,X1)
| ~ member(X2,singleton(X1))
| singleton(X1) = null_class ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_34,plain,
( member(X1,singleton(X1))
| singleton(X1) = null_class ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_35,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
c_0_31 ).
cnf(c_0_36,negated_conjecture,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
prove_corollary_2_to_universal_class_not_set_1 ).
cnf(c_0_37,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
c_0_32 ).
cnf(c_0_38,plain,
( ~ member(X1,X1)
| singleton(X1) = null_class ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
member(universal_class,universal_class),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( ~ member(X1,universal_class)
| member(X1,singleton(X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_17]) ).
cnf(c_0_41,negated_conjecture,
singleton(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_39])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET505-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/5.43 % Computer : n004.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Mon Sep 21 05:22:41 UTC 2026
% 0.17/5.43 % CPUTime :
% 0.17/5.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/5.47 Running first-order theorem proving
% 0.17/5.48 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/5.63 % Version: 3.5.1
% 0.20/5.63 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.20/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/5.63 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.20/5.63 % Starting new_bool_3 with 300s (1) cores
% 0.20/5.63 % Starting new_bool_1 with 300s (1) cores
% 0.20/5.63 % Starting sh5l with 300s (1) cores
% 0.20/5.63 % sh5l with pid 2325541 completed with status 0
% 0.20/5.63 % Result found by sh5l
% 0.20/5.63 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.20/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/5.63 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.20/5.63 % Starting new_bool_3 with 300s (1) cores
% 0.20/5.63 % Starting new_bool_1 with 300s (1) cores
% 0.20/5.63 % Starting sh5l with 300s (1) cores
% 0.20/5.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.20/5.63 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.20/5.63 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.20/5.63 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.20/5.63 % Starting SubtermCWHack with 28s (1) cores
% 0.20/5.63 % SubtermCWHack with pid 2325544 completed with status 0
% 0.20/5.63 % Result found by SubtermCWHack
% 0.20/5.63 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.20/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/5.63 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.20/5.63 % Starting new_bool_3 with 300s (1) cores
% 0.20/5.63 % Starting new_bool_1 with 300s (1) cores
% 0.20/5.63 % Starting sh5l with 300s (1) cores
% 0.20/5.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.20/5.63 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.20/5.63 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.20/5.63 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.20/5.63 % Starting SubtermCWHack with 28s (1) cores
% 0.20/5.63 % Preprocessing time : 0.001 s
% 0.20/5.63
% 0.20/5.63 % Proof found!
% 0.20/5.63 % SZS status Unsatisfiable
% 0.20/5.63 % SZS output start CNFRefutation
% See solution above
% 0.20/5.63 % Parsed axioms : 113
% 0.20/5.63 % Removed by relevancy pruning/SinE : 14
% 0.20/5.63 % Initial clauses : 99
% 0.20/5.63 % Removed in clause preprocessing : 0
% 0.20/5.63 % Initial clauses in saturation : 99
% 0.20/5.63 % Processed clauses : 2558
% 0.20/5.63 % ...of these trivial : 16
% 0.20/5.63 % ...subsumed : 1565
% 0.20/5.63 % ...remaining for further processing : 977
% 0.20/5.63 % Other redundant clauses eliminated : 9
% 0.20/5.63 % Clauses deleted for lack of memory : 0
% 0.20/5.63 % Backward-subsumed : 32
% 0.20/5.63 % Backward-rewritten : 24
% 0.20/5.63 % Generated clauses : 13158
% 0.20/5.63 % ...of the previous two non-redundant : 11278
% 0.20/5.63 % ...aggressively subsumed : 0
% 0.20/5.63 % Contextual simplify-reflections : 5
% 0.20/5.63 % Paramodulations : 13143
% 0.20/5.63 % Factorizations : 6
% 0.20/5.63 % NegExts : 0
% 0.20/5.63 % Equation resolutions : 9
% 0.20/5.63 % Disequality decompositions : 0
% 0.20/5.63 % Total rewrite steps : 4685
% 0.20/5.63 % ...of those cached : 4229
% 0.20/5.63 % Propositional unsat checks : 0
% 0.20/5.63 % Propositional check models : 0
% 0.20/5.63 % Propositional check unsatisfiable : 0
% 0.20/5.63 % Propositional clauses : 0
% 0.20/5.63 % Propositional clauses after purity: 0
% 0.20/5.63 % Propositional unsat core size : 0
% 0.20/5.63 % Propositional preprocessing time : 0.000
% 0.20/5.63 % Propositional encoding time : 0.000
% 0.20/5.63 % Propositional solver time : 0.000
% 0.20/5.63 % Success case prop preproc time : 0.000
% 0.20/5.63 % Success case prop encoding time : 0.000
% 0.20/5.63 % Success case prop solver time : 0.000
% 0.20/5.63 % Current number of processed clauses : 918
% 0.20/5.63 % Positive orientable unit clauses : 140
% 0.20/5.63 % Positive unorientable unit clauses: 9
% 0.20/5.63 % Negative unit clauses : 11
% 0.20/5.63 % Non-unit-clauses : 758
% 0.20/5.63 % Current number of unprocessed clauses: 8647
% 0.20/5.63 % ...number of literals in the above : 22797
% 0.20/5.63 % Current number of archived formulas : 0
% 0.20/5.63 % Current number of archived clauses : 56
% 0.20/5.63 % Clause-clause subsumption calls (NU) : 59199
% 0.20/5.63 % Rec. Clause-clause subsumption calls : 50471
% 0.20/5.63 % Non-unit clause-clause subsumptions : 1155
% 0.20/5.63 % Unit Clause-clause subsumption calls : 1606
% 0.20/5.63 % Rewrite failures with RHS unbound : 78
% 0.20/5.63 % BW rewrite match attempts : 45
% 0.20/5.63 % BW rewrite match successes : 23
% 0.20/5.63 % Condensation attempts : 0
% 0.20/5.63 % Condensation successes : 0
% 0.20/5.63 % Termbank termtop insertions : 168787
% 0.20/5.63 % Search garbage collected termcells : 227
% 0.20/5.63
% 0.20/5.63 % -------------------------------------------------
% 0.20/5.63 % User time : 0.123 s
% 0.20/5.63 % System time : 0.011 s
% 0.20/5.63 % Total time : 0.134 s
% 0.20/5.63 % Maximum resident set size: 3736 pages
% 0.20/5.63
% 0.20/5.63 % -------------------------------------------------
% 0.20/5.63 % User time : 0.127 s
% 0.20/5.63 % System time : 0.015 s
% 0.20/5.63 % Total time : 0.142 s
% 0.20/5.63 % Maximum resident set size: 4864 pages
% 0.20/5.63 % E exiting
%------------------------------------------------------------------------------